Polarizations on limiting mixed Hodge structures

TL;DR

This paper develops a polarization on the relative log de Rham cohomology groups of projective log deformations, analyzing filtrations and constructing a trace morphism to advance understanding of mixed Hodge structures.

Contribution

It introduces a new polarization construction for relative log de Rham cohomology in the context of projective log deformations, utilizing filtrations and trace morphisms.

Findings

Established a polarization on relative log de Rham cohomology

Analyzed the behavior of weight and Hodge filtrations under cup product

Constructed a trace morphism for log deformations

Abstract

We construct a polarization on the relative log de Rham cohomology groups of a projective log deformation. To this end, we study the behavior of weight and Hodge filtrations under the cup product and construct a trace morphism for a log deformation.